Knot theory and its applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Japanese |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
1996
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Japan. übers. |
| Beschreibung: | 341 S. graph. Darst. |
| ISBN: | 3764338172 0817638172 |
Internformat
MARC
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| 100 | 1 | |a Murasugi, Kunio |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Musubime-riron-to-sone-ōyō |
| 245 | 1 | 0 | |a Knot theory and its applications |c Kunio Murasugi |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1996 | |
| 300 | |a 341 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Noeuds, Théorie des | |
| 650 | 7 | |a Noeuds, théorie des |2 ram | |
| 650 | 4 | |a Knot theory | |
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Datensatz im Suchindex
| _version_ | 1804125388421464064 |
|---|---|
| adam_text | Contents
Introduction 1
« Fundamental Concepts of Knot Theory 5
1 The elementary knot moves 6
2 The equivalence of knots (I) 7
3 The equivalence of knots (II) 9
4 Links 14
5 Knot decomposition and the semi group of a knot 17
6 The cobordism group of knots 23
«Knot Tables 25
1 Regular diagrams and alternating knots 26
2 Knot tables 30
3 Knot graphs 34
¦^J^H Fundamental Problems of Knot Theory 40
^^^^H 1 Global problems 41
fll^B 2 Local problems 43
^J|V Classical Knot Invariants 47
^^^H 1 The Reidemeister moves 48
^PH^ft 2 The minimum number of crossing points 56
^ ^ 3 The bridge number 58
4 The unknotting number 61
5 The linking number 64
6 The colouring number of a knot 69
*^J//m Seifert Matrices 75
f^^| T The Seifert surface 76
^m^ 2 The genus of a knot 80
^ ^ 3 Tfo; Seifert matrix 83
4 S equivalence of Seifert matrices 89
^^¦^B Invariants from the Seifert matrix 104
WE^B 2 The Alexander polynomial 105
HH 2 The Alexander Conway polynomial 108
3 Basic properties of the Alexander polynomial 116
4 The signature of a knot 122
JBB Torus Knots 132
l^^l 1 Torus knots 133
fl|^B 2 The classification of torus knots (I) 137
3 The Seifert matrix of a torus knot 141
4 The classification of torus knots (II) 143
5 Invariants of torus knots 148
* Creating Manifolds from Knots 152
1 Dehn surgery 154
2 Covering spaces 159
3 The cyclic covering space of a knot 163
4 A theorem of Alexander 166
¦^Jf^m Tangles and 2 Bridge Knots 171
Wfi^H 1 Tangles 172
^ft^k 2 Trivial tangles (rational tangles) 176
3 2 bridge knots (rational knots) 182
4 Oriented 2 bridge knots 194
¦JfcW The Theory of Braids 197
^^9 1 Braids 198
^fl^ft 2 The braid group 201
~ ^ 3 Knots and braids 209
4 The braid index 214
^JK/m The Jones Revolution 217
J^^H 1 The Jones polynomial 219
fl|^B 2 The basic characteristics of the Jones polynomial 222
3 The skein invariants 231
4 The Kauffman polynomial 232
5 The skein polynomials and classical knot invariants.
(Alternating knots and the Tait conjectures) 241
* Knots via Statistical Mechanics 248
1 The 6 vertex model 249
2 The partition function for braids 255
3 An invariant of knots 260
¦^JjJH Knot Theory in Molecular Biology 267
¦j^^H 1 DNAandknots 268
^JH^^ 2 Site specific recombination 271
^^ 3 A model for site specific recombination 273
4 Recombination due to the recombinase Tn3 Resolvase 276
JIB Graph Theory Applied to Chemistry 284
^^^H 1 An invariant of graphs: the chromatic polynomial 286
^JK^k 2 Bing s conjecture and spatial graphs 289
3 The chirality of spatial graphs 296
^J^M Vassiliev Invariants 300
¦¦¦ 1 Singular knots 301
^V^H 2 Vassiliev invariants 304
3 Some examples of Vassiliev invariants 308
4 Chord diagrams 313
5 Final remarks 321
Appendix 325
Appendix (I): a table of knots 326
Appendix (II): Alexander and Jones polynomials 327
Notes 329
Bibliography 333
Index 337
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:00:46Z |
| institution | BVB |
| isbn | 3764338172 0817638172 |
| language | English Japanese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007288145 |
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| physical | 341 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
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| publisher | Birkhäuser |
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| spelling | Murasugi, Kunio Verfasser aut Musubime-riron-to-sone-ōyō Knot theory and its applications Kunio Murasugi Boston [u.a.] Birkhäuser 1996 341 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Aus dem Japan. übers. Knopentheorie gtt Noeuds, Théorie des Noeuds, théorie des ram Knot theory Knotentheorie (DE-588)4164318-5 gnd rswk-swf Knotentheorie (DE-588)4164318-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007288145&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Murasugi, Kunio Knot theory and its applications Knopentheorie gtt Noeuds, Théorie des Noeuds, théorie des ram Knot theory Knotentheorie (DE-588)4164318-5 gnd |
| subject_GND | (DE-588)4164318-5 |
| title | Knot theory and its applications |
| title_alt | Musubime-riron-to-sone-ōyō |
| title_auth | Knot theory and its applications |
| title_exact_search | Knot theory and its applications |
| title_full | Knot theory and its applications Kunio Murasugi |
| title_fullStr | Knot theory and its applications Kunio Murasugi |
| title_full_unstemmed | Knot theory and its applications Kunio Murasugi |
| title_short | Knot theory and its applications |
| title_sort | knot theory and its applications |
| topic | Knopentheorie gtt Noeuds, Théorie des Noeuds, théorie des ram Knot theory Knotentheorie (DE-588)4164318-5 gnd |
| topic_facet | Knopentheorie Noeuds, Théorie des Noeuds, théorie des Knot theory Knotentheorie |
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